Solve for $k$. Give an exact answer. $2.5(4k+2)=12k$ $k =$
Answer: We need to manipulate the equation to get $ k$ by itself. $\begin{aligned} 2.5(4k+2) &= 12k \\\\ 10k+5 &= 12k~~~~~~~~~~\gray{\text{Distribute}}\\\\ 10k+5{-10k} &= 12k{-10k} ~~~~~~~~~~\gray{\text{Subtract 10k from each side}}\\\\ 5&=2k ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{5}{{2}}&= \dfrac{2k}{{2}}~~~~~~~~~~\gray{\text{Divide each side by 2}} \\\\ k &= {2.5} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ k= { 2.5 }~~~~~~~~$ [Let's check our work!]